The government is considering giving away 225 million pounds of surplus American cheese--a pound apiece for every man, woman and child in the country.

The specter of a growing cheese accumulation under the federal dairy price support system, with its potential for spoilage and huge financial losses, has sent Agriculture Department planners into a flurry of brainstorming over ways to reduce the surplus.

USDA officials acknowledge they are desperate to get rid of excess cheese but they haven't yet figured out how to do it.

One complicated option, to distribute free cheese in grocery stores through some sort of coupon system, was shelved at USDA after supermarket operators refused to go along.

Another option reportedly scheduled for discussion at a closed meeting yesterday of the directors of USDA's Commodity Credit Corp. (CCC) would entail distribution of the surplus cheese to food-stamp recipients.

CCC officials are not expected to make a decision for some time. In fact, they are not even certain they have the legal authority to simply give away the cheese--one of the options that could save on storage costs and avert spoilage loss. Dairy-surplus storage and interest cost the government about $1 million a day.

But that's not all. The processed American cheese, acquired at a cost of roughly $331 million during the last 18 months under the support program, is only about half of CCC's stock. It also has more than 330 million pounds of natural cheese, which, although it keeps longer than processed cheese, must be disposed of in the future.

Dairy production continues upward at a steady pace, although the Reagan administration has moved vigorously to cut back the support program. CCC acquisitions of surplus cheese, butter and non-fat dry milk are expected to cost about $1.1 billion during fiscal 1982.

Earlier this week at the White House, Agriculture Secretary John R. Block displayed two hunks of moldy cheese to highlight the administration's push for its cutback plan, which is deadlocked in a House-Senate conference on a new farm bill.

"Nobody really knows the storage life of this processed cheese," said Indulis Kancitis, of the dairy branch of the Agricultural Stabilization and Conservation Service (ASCS), the overseer of the commodity support programs. "People say it should last two years, but it is developing mold--although that doesn't mean it is spoiled. Most of this surplus has been acquired since June, 1980."

CCC and ASCS considered the option of supermarket distribution of free cheese in part because it comes in five-pound bricks, a size suitable for easy handling. But the Food Marketing Institute, representing most supermarkets, objected.

Karen Brown, a vice president of the institute, said, "The government has a real problem with this perishable product and they have to move it out. But our members have problems with their moving it through retail outlets--problems of customer relations, distribution, supply and redemption of the coupons they wanted to use."

Another side to giving away the cheese through retail outlets is that it really wouldn't solve much. Sales displacements--not welcomed by the grocers or cheese manufacturers--would only mean that more new unmarketable surplus would have to be acquired by the CCC under the federal support program.

Robert Anderson, executive director of the National Cheese Institute in Chicago, said his cheese-makers' trade group is concerned about market disruptions if the CCC unloaded its cheese to the general public.

"The cheese is there," Anderson said, "and we recognize that it must be kept in storage. And we feel that it should be used, but not to disrupt the commercial market. Our recommendation is that it would be eminently practical to distribute it to food-stamp recipients. That is how the food-stamp program began, with surplus food distribution. This is a food that should be used and we think they could set up a system of reasonably easy distribution."

Some other options being considered include sending more cheese to school lunchrooms, feeding programs for the elderly or urban food banks, but most of these do not have adequate storage space. The cheese institute's idea of sending some of it to economically troubled Poland, with poor credit and little storage capability, has been considered but generally discarded, USDA sources said.

Added another USDA official: "We've looked and looked at ways to deal with this, but the distribution problems are incredible. And you cannot permit a disruption of sales. Probably the cheapest and most practical thing would be to dump it in the ocean."